Question

An electron in a long organic molecule used in a dye
laserbehaves approximately like a 1D particle in a box with a
length of3.78 nm (the length of the molecule). What is the
wavelength of thephoton emitted when the electron undergoes a
transition from thefirst excited state to the ground state?

Note: I don't think the length in the problem is relevant
buti'm not sure about it.

My work:

For the first excited state:

For the ground state:

The change in energy is:

So now the wavelength is found from:

Show transcribed image textAn electron in a long organic molecule used in a dye laserbehaves approximately like a 1D particle in a box with a length of3.78 nm (the length of the molecule). What is the wavelength of thephoton emitted when the electron undergoes a transition from thefirst excited state to the ground state? Note: I don't think the length in the problem is relevant buti'm not sure about it. My work: For the first excited state: For the ground state: The change in energy is: So now the wavelength is found from: